Prediction of the sound field in large urban environments has been limited thus far by the heavy computational requirements of conventional numerical methods such as boundary element (BE), finite-difference time-domain (FDTD), or ray-tracing methods. Recently, a considerable amount of work has been devoted to developing energy-based methods for this application, and results have shown the potential to compete with conventional methods. However, these developments have been limited to two-dimensional (2-D) studies (along street axes), and no real description of the phenomena at issue has been exposed (e.g., diffraction effects on the predictions). The main objectives of the present work were (i) to evaluate the feasibility of an energy-based method, the diffusion model (DM), for sound-field predictions in large, 3-D complex urban environments, (ii) to propose a numerical hybrid method that could improve the accuracy and computational time of these predictions, and (iii) to verify the proposed hybrid method against conventional numerical methods. The proposed numerical hybrid method consists of a full-wave model coupled with an energy-based model. The full-wave model is used for predicting sound propagation (i) near the source, where constructive and destructive interactions between waves are substantial, and (ii) outside the cluttered environment, where free-field-like conditions apply. The energy-based model is used in regions where diffusion conditions are met. The hybrid approach, as implemented in this work, is a combination of FDTD and DM models. Results from this work show the role played by diffraction near buildings edges close to the source and near the exterior boundaries of the computational domain, and its impact on the predictions. A wrong modeling of the diffraction effects in the environment leads to significant under or overpredictions of the sound levels in some regions, as compared to conventional numerical methods (in these regions, some differences are as high as 10 dB). The implementation of the hybrid method, verified against a full FDTD model, shows a significant improvement of the predictions. The mean error thus obtained inside the cluttered region of the environment is 1.5 dB. / Master of Science

Ce mémoire de thèse présente le développement de la méthode «statistical modal energy distribution analysis (SmEdA)» pour des systèmes vibro-acoustiques couplés. Cette méthode de calcul est basée sur le bilan énergétique dans des sous-systèmes fermés couplés, comme une structure ou une cavité. L’interaction entre de tels systèmes est décrite par des couplages entre les modes. La version initiale de SmEdA prend en compte seulement les modes qui ont une fréquence propre dans le bande d’excitation. Le travail présenté ici étudie l’effet des modes non résonants sur la réponse et identifie les cas dans lesquels un tel effet devient important. L’introduction des modes non résonants permet d’utiliser la méthode SmEdA dans des cas d’applications plus larges. En outre, une nouvelle méthode de post-traitement a été développée pour calculer des distributions d'énergie dans les sous-systèmes. Finalement, une nouvelle méthode d'approximation pour la prise en compte des modes de systèmes de grandes dimensions ou mal définis a été formulée. Toutes ces méthodes ont été comparées avec d’autres méthodes de calcul via des exemples académiques et industriels. Ainsi, la nouvelle version de SmEdA incluant le post-traitement pour obtenir des distributions d'énergie a été validé et les avantages et possibilités d'applications sont montrés. / This dissertation presents the further development of the statistical modal energy distribution analysis (SmEdA) for vibro-acoustic coupled problems. This prediction method is based on the energy balance in bounded coupled subsystems, like a structure or a cavity. The interaction between such subsystems is described by mode-to-mode coupling. The original SmEdA formulation takes into account only the modes having the eigenfrequencies within the excitation band. The present work investigates the effect of non resonant modes to the response and identifies cases in which such an effect becomes important. The inclusion of non resonant modes has thus resulted in a new SmEdA formulation which can be used in extended applications. Furthermore, a new post-processing method has been developed to predict energy distribution within subsystems. Finally a novel approximation method for handling modes of huge or ill-defined systems has been formulated. All these methods have been compared to other prediction methods via academic and industrial examples. In this way, the extended SmEdA approach including the post-processing for energy distribution has been validated and its advantages and application possibilities have been demonstrated.